Further Mathematics 7367: Polar Coordinates Topical Past Paper Questions

The curve C has polar equation $ r = 2 + \tan\theta $ The curve C meets the line $ \theta = \frac{\pi}{4} $ at the point A The point $B$ has polar coordinates $(4, 0)$ The diagram shows part of the curve C, and the points A and B (q) Show that the area of triangle OAB is $ 3\sqrt…

The curve C has polar equation $$ r=\frac{4}{5+3\cos\theta}\qquad(-\pi<\theta\leq\pi) $$ Show that $r$ takes values in the range $\frac{1}{k} \leq r \leq k$, where $k$ is an integer. [2 marks] ) Find the Cartesian equation of C in the form $ y^2 = f(x) $ [4 marks] (c) The ellipse…

Roberto is solving this mathematics problem: Roberto's solution is as follows: $$ \begin{array}{c}A=\displaystyle\frac{1}{2}\int_{-\pi}^{\pi}9\sin2\theta~\mathrm{d}\theta\\=\displaystyle\left[-\frac{9}{4}\cos2\theta\right]_{-\pi}^{\pi}\\=0\end{array} $$ Sketch the curve $C_{1}$ […